Non-equilibrium parameter for a hybrid Fokker-Planck/ DSMC scheme

Abstract

Numerical simulation of hypersonic rarefied gas flows requires modelling of non-equilibrium flow phenomena, like e. g. shock waves. While such non-equilibrium flows can be simulated by the highly accurate direct simulation Monte-Carlo (DSMC) algorithm, computational effort for DSMC increases quadratically with decreasing Knudsen numbers. Therefore it is a common practice to couple DSMC with less accurate, but more efficient flow solvers in areas where the resolution of DSMC is not required. A recent approach for such a flow solver employs the kinetic Fokker-Planck (FP) model. Like in DSMC, the FP model simulates the stochastic motion of a set of particles through the computational domain which suggest a simple coupling of both methods. No collisions must be calculated in the FP approach and so larger cell and timestep sizes than by DSMC calculations can be used. Because of this, the FP model holds the potential to be more efficient than DSMC where Knudsen number is small. Here, a hybridization scheme for the FP and DSMC algorithms is presented.